J. Frehse et J. Naumann, ON WEAK SOLUTIONS TO THE NONSTATIONARY VAN-ROOSBROECK SYSTEM WITH DISCONTINUOUS PERMITTIVITIES, Mathematical methods in the applied sciences, 20(8), 1997, pp. 689-706
In this paper we prove the existence of a weak solution to the non-sta
tionary drift-diffusion equations (van Roosbroeck's system) of semicon
ductor theory involving discontinuous permittivities. The proof is bas
ed on an approximation of these equations by a system with bounded non
-linearities, deriving a priori estimates on the approximate solutions
and then carrying out the passage to limit. The discussion is complet
ed by some regularity results for the weak solution under consideratio
n. (C) 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.